Question

A hyperbola in the form (x ^ 2)/(a ^ 2) - (y ^ 2)/(b ^ 2) = 1 has a center, vertices, and foci that fall along a horizontal. Please select the best answer from the choices provided. True or false

Answer 1

Answer:

True

Step-by-step explanation:

Explanation:-

The equation of the standard hyperbola is  

                         $\frac{x^{2} }{a^{2} } - \frac{y^{2} }{b^{2} } =1$

•       Center is (0,0)

• Hyperbola is symmetric with respective to both the axes, since if (x, y) is a point on the hyperbola, then (-x, y), (-x,-y), (x,-y) are also lie on the parabola.
• The relation of between focus and transverse and conjugate axes c²=a²+b²

• The transverse axis is along x-axis  

• The conjugate axis  is along y-axis
• The length of transverse axis is 2 a
• The length of conjugate axis is 2 b
• The foci is (±c,0) and the equation of foci is x=±a e)

• The length of Latus rectum is $\frac{2b^{2} }{a}$